1. Field of the Invention
The present invention relates to devices for controlling the operation of scanning beam systems. More particularly, the present invention relates to devices for regulating the operation of ultrasonic beam transmitters. Still more particularly, the present invention relates to devices for controlling the positioning and alignment of an ultrasonic beam in two or three dimensions of translation and two dimensions of angular tilt. The invention has particular application in the field of non-intrusive medical analysis devices but is not limited thereto.
2. Description of the Prior Art
The only ultrasound-aiming device of the prior art resembling the present invention is taught by Seale in U.S. Pat. No. 5,844,140: "Ultrasound Beam Alignment Servo." In one embodiment of that invention, illustrated here in FIG. 1, reproduced from FIG. 13 of the prior art patent, Seale teaches a system of air core coils 1330, 1331, 1332, 1333, and 1334, surrounding a water-filled cavity, shown inside cylindrical wall 1322 and above base 1324. The enclosing ultrasound window is removed from the top and not shown, but is normally present and brought in contact with a patient for operation. Within that cavity floats a neutrally-buoyed rotor 1302 containing an ultrasound transducer 1301 and a permanent magnet 1305. The ultrasound transducer is connected to an external ultrasound signal generation and reception system (not shown) by way of a tether cable 1320 of fine flexible wire following a spiral path from the rotor to the side of the water-filled cavity. The magnetic fields produced by the air core coils in the housing exert linear and torsional forces on the magnet in the rotor, causing the rotor to translate and rotate controllably, thereby altering the position and angular alignment of the ultrasound beam from the transducer in the rotor. Magnetic measurements lead to determination of the position and orientation of the rotor, permitting the closure of a multidimensional feedback loop to bring the rotor to a desired position and orientation. The result is to position and align the ultrasound beam emerging from the rotor. One of the potential uses of that prior art system is transcranial ultrasound Doppler, for which an ultrasound transducer needs to be moved in translation and rotation until a partially ultrasound-transparent window is found in the human skull. The ultrasound beam is aligned through this window to insonate a cranial artery with frequency bursts and to receive back Doppler echo signals. Seale's system of the prior art is discussed in some detail here, since the current invention was developed specifically to overcome limitations of the prior art system--limitations severe enough to preclude practical clinical use. The background given here will clarify the context of and necessity for the described improvements. The prior art system in question, while suffering severe deficiencies in an application requiring significant lateral rotor translations in a plane, provides a basis for development of the current invention. In applications requiring levitation of an ultrasound rotor with two-axis rotation but very limited translation, the system of prior art is effective and does not require the invention taught herein. A review of U.S. Pat. No. 5,844,140 provides useful background for the current Specification.
In the prior art, Seale teaches two alternative methods for detecting the position and alignment of the rotor, in order to close feedback loops to control its position and alignment. The first uses an AC magnetic beacon, and the second senses of the field of the permanent magnet in the rotor using multiple sensors in the stator. The DC method will be summarized first, followed by the AC method, in two variations. It will be shown that of the three approaches, only one provides an adequate starting basis for use with a rotor that must translate over significant distances in a plane. The Specification to follow this section will show how severe inadequacies of the most favorable system approach of the prior art are overcome to produce a useful clinical instrument.
The DC field-sensing approach to determination of rotor position/orientation taught in the prior art by Seale takes advantage of inexpensive Hall effect sensors, 1340 through 1347 in FIG. 1. These sensors include a Hall effect bridge circuit responsive to magnetic fields cutting across the plane of the bridge, plus a sensitive amplifier to raise the extremely small bridge output voltage to a useful signal level. This approach was taught as a preferred embodiment for the system most resembling the present invention, and illustrated here in FIG. 1, achieving 5-axis control over translation in x, y, and z, plus tilt of the magnetic dipole axis from a center z-axis direction to give projection into the x and y planes. Because of symmetry, rotation of the rotor magnet about its dipole axis does not affect the detected external magnetic field. Such a rotation cannot be driven by external coils. Thus, rotation about a third axis is not a degree of freedom of the control system in any of the variations described in any detail here or in the prior art reference. Hence, with the exception of systems that might gain control of rotation about a third axis through quadrupole magnetic interactions, most systems for full levitation and tilt control will be 5-axis systems. By using more Hall sensors than the number of degrees of freedom to be determined for rotor position/orientation, e.g., 8 sensors for 5 degrees of freedom in the prior art example shown here in FIG. 1, it was taught to use "redundant" information in the set of magnetic signals to measure and cancel the variable effect of the geomagnetic field and similar steady or varying magnetic fields from distant objects. Specifically, any field whose flux lines are substantially straight and parallel passing through the assembly of FIG. 13 was rejected.
This detection approach to position/orientation works well in practice for rotors that undergo minimal translation, such that the Hall sensors can be located quite close to the levitated rotor. If the rotor translates significantly, and especially if the translation is two-dimensional, covering a significant extent over an (x,y) plane (as in the prior art example shown in FIG. 1), or three-dimensional, covering a significant volume, then of necessity the distance from the rotor magnet to a given Hall sensor varies considerably. As was taught in the prior art, if the coils are to be made compact and are to surround a cavity of significant extent in two or three dimensions, then those coils cannot lift a magnet against gravity without overheating. The solution taught for the overheating problem was to enclose the rotor magnet and ultrasound transducer in a hollow shell, sized to float with neutral buoyancy in an ultrasound transmission fluid, thus offsetting gravity and permitting the rotor to be levitated and moved by very small magnetic forces and torques. Illustrated rotor 1302 of FIG. 1 has the proper proportions for neutral buoyancy. A consequence of this design approach is that the dense rotor magnet 1305 occupies a small fraction of the rotor volume in order to achieve neutral buoyancy, while the rotor itself occupies a small fraction of the volume of the cavity in which it moves. It is well known that the field from a magnetic dipole attenuates inversely as the cube of distance. Hence, the order-of-magnitude of attenuation of the field strength of a permanent magnet, in going from the magnet surface to the surface of the rotor cavity, is on the order of the ratio of the magnet volume to the cavity volume, starting from a magnet surface field strength, which is normally below one Tesla. When the rotor travels from a center position to an edge of its cavity, some of the Hall sensors will end up being roughly twice as far from the magnet, implying an additional 8-to-1 field attenuation. Other sensors, being found more than two times closer to the rotor magnet after a movement of the rotor off center, will see more than an 8-to-1 increase in field strength. Hence, the Hall sensors need to respond with good signal/noise ratio over a dynamic range exceeding 64-to-1. Differential sensitivity of a Hall sensor to change in magnet position varies as the field gradient, which attenuates inversely as the fourth power of distance, i.e. more severely than the field strength itself. Even if Hall sensors were free of noise and drift, which they are not, the large dynamic range indicated here would still present challenges for AND conversion.
Compounding the dynamic range problem is a high noise floor for the sensitivity of solid state Hall effect devices, arising from the physical nature of their detection process. For reasonable current density and tolerable local heating in a Hall sensor bridge, the bridge output voltage is measured in microvolts for field strengths on the order of one Tesla. Thermal agitation establishes a noise floor for the bridge output voltage, regardless of the performance of the amplifier that brings the bridge output up to a useful level. Given the maximum strength of available permanent magnet materials, coupled with the inevitably large magnetic field attenuation factors described above, one finds that a small set of Hall sensors (e.g., the set of eight sensors taught in the prior art patent) cannot accurately resolve the position of a neutrally buoyant magnet-carrying rotor having latitude for significant two-axis translation in a cavity. In the best achievable realization of the system, the levitated rotor is observed to jitter and drift in position and orientation due to disturbances that trace back to temperature gradients across the Hall bridges, to amplifier noise and drift, and to Johnson noise in the Hall sensor bridges. As the rotor moves away from a central position, causing some Hall sensors to operate in a less sensitive range, servo performance deteriorates further.
Low-level position/orientation detection works much better with a beacon coil than by a Hall sensor approach, because of limitations related to the physics of the Hall sensor. Radio receivers routinely detect extremely low signal levels at high frequencies. The drive coils in a levitating servomechanism perform very well as antennas for receiving a beacon signal. In the prior art, Seale taught that the multiple beacon signals received by the multiple drive coils in such a system effectively define non-linear position coordinates for the translational and rotational degrees of freedom of the rotor. In more detail, a beacon coil in the levitated rotor generates a high frequency AC magnetic field, which induces AC voltages in the surrounding drive coils. Each drive coil or set of coils is driven by a voltage amplifier. A transformer wired in series with the amplifier output passes the low frequency drive signal from the amplifier to the driven coil or coils, while high frequency current induced in the coil by the rotor beacon encounters an inductive impedance in the transformer. The AC voltage thus generated and sensed in the transformer secondary winding is amplified and demodulated, using the beacon carrier for synchronous demodulation, resulting in a base band signal that is a beacon coordinate associated with the mutual inductance interaction of the drive coil circuit with the beacon coil in its current position and orientation. It was taught that if the center position and orientation of the AC dipole represented by the beacon coil is conveniently made to match the center and orientation of the magnet or collection of permanent magnets in the rotor, then the strength of the beacon signal induced in a given drive coil circuit is proportional to the strength of the energy coupling between the current in that circuit and a magnetic interaction energy in the rotor magnet or magnet collection. This coupling, measurable with the beacon signals induced in the drive coils and expressible in units of joules per ampere (i.e. joules of magnetic interaction energy per ampere of current in a given coil or coil arrangement), is designated a "beacon coordinate." The derivative of a beacon coordinate with respect to linear position represents a linear force-perampere, while the derivative of a beacon coordinate with respect to angle represents a torsional force-per-ampere. Hence, beacon coordinates map couplings of generalized forces, which are taken to include both linear forces and angular or torsional forces. By proper placement of a beacon coil in relation to a magnet, beacon coordinate mappings correspond accurately to mutual inductance mappings, which forms the basis for measuring beacon coordinates through measurement of induced voltages. Thus, a mapping that forms a practical basis for position measurement can be made almost indistinguishable from a mapping that describes the force couplings used to change measured position.
In the prior art, Seale taught that, even when a system of beacon coordinates is very nonlinear in comparison with, e.g., Cartesian coordinates and tilt direction cosines, one can still close servo control loops with respect to the beacon coordinates of a rotor and achieve a convergent servo system. Furthermore, if there are more beacon coordinates than degrees of freedom of the system, corrective feedback loops through all the beacon coordinates can still be used for servo control in an "overdetermined" system. The advantage of redundant control in an overdetermined system is that even if energy couplings via some beacon coordinates become quite weak for certain rotor positions and orientations, those coordinate couplings that remain strong will dominate the control interaction and can cause the system to converge. Hence, a servo with five degrees of freedom, three in translation and two in tilt angle, can use more than five drive coils, each associated with a beacon coordinate and a servo control loop.
The targets for the beacon coordinates of a rotor can be generated in analog fashion using a joystick system whose beacon coil and detection coils are laid out in the same geometry as the rotor to be controlled. Thus, when the rotor is "asked" to move to the same beacon-coordinate "position" as the joystick, and all the beacon coordinate differences between rotor and joystick are amplified and sent out through the rotor drive coils, then the rotor position will be driven toward a match with the joystick position and can be made to track the joystick. A system accomplishing this has been implemented combining the coil geometry illustrated in FIG. 1 from the prior art with the AC beacon coil approach to determination of the beacon coordinates. The levitated rotor in such a system does in fact track the position of a joystick carrying a beacon coil and inserted into a set of coils matching the coils around the rotor. Problems encountered with that system and overcome with the current invention will be described below. The joystick signal vector, i.e. the collection of beacon coordinates representing joystick position, with possible redundancy, can be generated by computation rather than by direct analog interaction of coils with a physical joystick carrying a beacon coil.
Using the AC beacon approach, a beacon coil in the rotor is excited and caused to generate an AC magnetic field, typically at a frequency well above the mechanical response bandwidth of the servomechanism but well below the ultrasonic range used by the transducer, e.g., 50 kHz. As was taught in the prior art, the beacon coil can be excited by a signal voltage carried to the levitated rotor via a tether cable, of the coil can consist of a shorted conductive loop or shorted winding exposed to an external electromagnetic excitation field, resulting in an "induced beacon." In the induced beacon approach, the detected beacon signal is actually a detected perturbation in the excitation field, caused by the presence of the shorted loop and sensitive to the position and orientation of the shorted loop. If the ultrasound rotor volume is small compared to the volume of the cavity in which the rotor travels, then the "induced beacon" perturbation attributable to the rotor is of necessity weak. The system for determining rotor position is consequently sensitive to perturbing influences other than the rotor, e.g. to eddy currents induced in nearby metallic objects and to magnetic fields induced in nearby ferromagnetic objects. While the induced beacon approach is useful for a rotor confined to minimal translation in a nest of tightly-coupled stator coils, especially where this approach eliminates necessity for a tether to the rotor (e.g. where the rotor acts as a movable reflector of an ultrasound beam), this approach is not useful in the present context of a levitating rotor intended to travel significant distances in translation. Further discussions will therefore concern only beacon coils excited by a signal brought in via a tether wire.
The purpose of the invention to be taught below is to overcome significant problems and limitations of the nonlinear beacon coordinate feedback control system taught in the prior art. The problems concern nonlinearity and singularity in the beacon coordinate system of the device taught for 5-axis control with a large range of translation in an (x,y) plane. In the prior art, it was suggested that signals detected in Hall sensor coordinates could be translated into the beacon coordinates describing the interactions of drive coils and the rotor magnet. As was indicated above, limitations in the Hall sensors preclude high quality realization of the above goal. The system functions, but only marginally. We will therefore concentrate on systems based on an AC beacon coil in a levitating rotor attached by a tether. Detection of position/orientation in such systems is far more robust than with Hall sensors, for two reasons. First, drive coils make excellent antennas for the beacon signal from a levitating rotor, and synchronous demodulation of the resulting antenna signal can be accomplished with excellent linearity, dynamic range, and a low noise floor. Second, inverse-cube-law relations do not apply to the coupling between a small beacon coil and a large and partly encircling drive coil. The inverse cube law applies only to a transmitter and antenna separated by distances significantly larger than the size of either the transmitter or antenna. A drive coil extended in space around a rotor and beacon coil responds to the position and orientation of that coil within a smaller dynamic range than a "point" sensor. Thus, AC beacon signals picked off drive coils are easier to use than Hall sensor signals.
Even given the advantage of coils over point sensors, there is considerable gain variation around a servo feedback loop designed for 5-axis levitation with significant translation. As the beacon coordinate varies with rotor position/orientation, the sensitivity or differential gain for position/orientation detection varies, and the sensitivity or differential gain for actuation, driving changes in position/orientation varies, in the same proportion. The net loop differential gain, being the product of detection gain and actuation gain, therefore varies as the square of the sensitivity of the beacon coordinate to the controlled component of rotor motion. The servo control loop drives an inertial load, meaning that a coil current establishes a component of linear and/or angular acceleration in the load. Such a second order servo system requires some form of damping or phase-lead compensation to achieve good settling to a target position. For precise control of multidimensional position, a component of integral gain is commonly added to the control loop transfer function. "PID" control, for Proportional, Integral, and Derivative components of loop gain, is.described in Seale's prior art teaching. When differential loop gain for a given servo control channel varies widely, however, then a PID control loop behaves poorly. Loop gain variations with changing rotor position alter the "P" "I" and "D" gains by the same multiple, yet among the three gain terms, the proportions yielding the best settling response change as the overall gain changes. The most obvious adverse consequence arises when a controller is optimized for a given gain between beacon coordinate variation and corresponding linear translation or rotation of an inertial mass, and that beacon coordinate gain is reduced. First, the reduction factor is squared, since (as discussed above) the gain reduction hits the control loop twice, once for sensing and once for actuation. A gain reduction causes the system to be underdamped and to have an excessively high integral gain. Both effects contribute to system overshoot and ringing in what would be described as a very sluggish "loose" control loop. An excessive integral component of loop gain can contribute to growing oscillations, and even if recovery from small perturbations converges, integral loop gain can slow overload recovery, especially when the ultrasound rotor bumps a solid surface, leading to blocking oscillations. A high loop gain leads to an overdamped situation, which would not be considered a problem since the time scale of the system response is reduced, so that settling time is not too large. Yet, too much increase in loop gain leads to instability and oscillations at higher frequencies due to higher order phase lags and information delays around the loop. The most obvious higher order phase lag involves coil inductance. At low frequencies, coil drive voltage establishes a proportional current in a coil. At higher frequencies, as inductive impedance in the coil comes to dominate resistance, the coil drive voltage begins to establish the rate-ofchange of current, implying additional phase lag in the control loop. If coil current is controlled by a current amplifier rather than a voltage amplifier, then the gain around the servo loop goes from +6 db/octave for the damping term of the PID controller to +12 db/octave due to the voltage developed to overcome inductance. Information delay arises because position feedback information based on demodulation of a beacon carrier signal comes in pulses with gaps in-between, where position is not being updated. Lowpass filtering of the demodulator output makes the output appear continuous, but this is achieved at the cost of added phase delay. It might appear that carrier ripples propagating through a control loop would be inconsequential. In fact, severe high frequency problems arise if signals approaching half the carrier frequency are not filtered aggressively.
Even though the sluggishness of the mechanical response causes the electromechanical loop gain to fall with increasing frequency even as the electronic gains rise, unintended high frequency couplings come into play. In particular, a demodulator in the system is intended to respond to voltages induced by the beacon coil in a given drive coil. The demodulator also responds to high frequency components coming directly from the amplifier driving the coil. As feedback gains are pushed up, and as phase-lead compensation terms are piled on to maintain good damping at high proportional gains and overcome higherorder phase lags such as inductance, then the gain from the demodulator output around to its own input, via the drive amplifier, increases steeply. A signal at half the beacon carrier frequency, when demodulated against the beacon carrier, produces a new signal at half the carrier frequency. Frequencies below this half-carrier frequency bounce up above half the carrier frequency after demodulation, and frequencies above bounce down below half the carrier frequency. Suppose that one wants a worst-case servo settling speed equivalent to a 5 Hz bandwidth, which is marginally fast enough to not feel sluggish to a human operator. In a highly nonlinear servo controller as taught in Seale's prior art patent, differential beacon coordinate gain with respect to a linear coordinate of position or rotation will easily vary by 20-to-1. This implies a 400-to-1 variation in servo loop gain. Thus, to maintain control to 5 Hz bandwidth in regions of weak electromagnetic coupling, one ends up setting proportional electronic gains 400 times higher than are required for the most sensitive rotor positions. To provide critical damping where beacon coordinate slope is the lowest, one requires phase lead compensation coming into play at the frequency corresponding to the minimum settling bandwidth, e.g., 5 Hz. Thus, one begins to push up high frequency gains starting from a very low frequency. If the phase lead compensation is rolled off with a pole at a moderately higher frequency, e.g., 20 Hz, then the system starts to ring badly around 20 Hz for rotor positions where the beacon coordinate slope is high. As one pushes the lowpass poles up the frequency scale to attain damped servo response and avoid instability at high-gain rotor positions, one quickly reaches a situation where, e.g., with a beacon carrier frequency at 50 kHz, regenerative oscillations are being generated at 25 kHz as drive amplifiers talk to demodulators. Pushing to a substantially higher carrier frequency introduces new problems. When drive coils are packed in close proximity, capacitive couplings between them introduce cross talk. This effect increases very rapidly with increasing frequency. Another constraint for compatibility with Doppler sonar systems is keeping the beacon carrier frequency synchronized with a common denominator of the pulse intervals used for various depths of operation. In a typical transcranial Doppler context, one cannot use a beacon carrier frequency much higher than the 50 kHz range.
The constraints described above imply great difficulties in achieving a servo control system that settles consistently, through its range of rotor positions, even for an equivalent bandwidth of only 5 Hz. The problem concerns primarily regions of low slope of the beacon coordinates with respect to linear coordinates. Even with adaptive electronic gain to avoid problems of excess gain at sensitive beacon coordinate regions, practical limitations in gain around the beacon coordinate servo loop prevent good response.
This problem is compounded by another problem alluded to in Seale's prior art patent, but whose severity was perhaps not fully appreciated: mapping singularity. As beacon coordinates bend, positions in 5-space (for the degrees of freedom in translation and rotation) arise for which the beacon coordinates are far from mutually orthogonal. Singularity arises when no combination of drive signals will produce a generalized force (in a coordinate space of linear and torsional forces) along a particular axis, or cannot generate such a force without simultaneously generating an unwanted force component along another axis. At or near a singularity, a controller cannot control motion independently, or at all, for one or more axis directions. In a prior art coil topology like that illustrated here in FIG. 1, but in a system using an AC rotor beacon coil, coil excitation via tether wiring, and demodulation of induced coil voltages to derive beacon coordinate signals, two singularities appeared in mirror-image positions. They appeared when the rotor was translated to nearly a maximum distance from one of coils 1330 or 1331 and simultaneously tilted such that the magnet in the bottom of the rotor moved, by way of rotation and its off-center location in the rotor, still farther off-center. While experimental observation of the rotor becoming uncontrollable in that region led to a suspicion that the rotor magnet was simply too far from one of the drive coils, a mathematical analysis of the magnetic field structure revealed a true singularity in the matrix of partial derivatives relating beacon coordinates to linear and angular coordinates. With a singularity, all five coils have some "purchase" on the spatial region in question, but no combination of signals from the five coils can provide "purchase" for motion in some particular coordinate direction. In terms of servo performance, motion in that particular direction becomes totally uncontrollable at the singular point and only weakly controllable near the singular point. The same prototype system demonstrated instability when the rotor translated and rotated to bring the magnet and surrounding beacon coil close to the cusp where coils 1330 and 1331 meet. Similar problems have been observed elsewhere near the cusps between abutting coils. It has not been determined whether these are problems of singularity as described above, or problems having to do with extreme curvature of the magnetic fields in a cusp region. In the prior art patent, it was proposed to add redundant coils with associated redundant beacon coordinates and control channels in order to cover the "weak" regions surrounding singular points in the beacon coordinate mapping. Extra coils and control channels were expected to "fill in the gaps" around singularities of a non-redundant system. A redundant coil and associated circuitry to define another beacon coordinate eliminated the mirror-image singularities described just above, but did not eliminate the stability problem near the cusp between abutting coils 1330 and 1331. Whatever further analysis might reveal about this problem, it is clear that the strongly curving fields around cusps between abutting coils, and the corresponding highly nonlinear regions of a beacon coordinate mapping, are best avoided for a well-behaved levitating servo design.
When redundant beacon coordinates are used, problems arise with integral gain in the servo channels. If the servo system can "solve itself" for as many servo coordinates as there are controllable degrees of electromechanical freedom, then the integrator outputs converge to bounded values consistent with keeping the rotor at the desired position and orientation. With redundant coordinates, the system never "solves itself" exactly in all the redundant coordinates, due to inconsistencies between the system than generates targets in redundant coordinates (e.g., a joystick having 5 degrees of mechanical freedom and 6 or more output voltages representing the redundant coordinates) and the actuator/sensor system that is required to match all the channels. For integral control, one must boil the redundant coordinates down to the correct non-redundant number, reflecting the mechanical degrees of freedom. When one does so, the system converges with poor accuracy and repeatability in regions that are nearly singular in the non-redundant coordinates of integral feedback control. Where redundant coordinates are employed, one ends up with extra servo loops and complex blending of non-redundant integral control with redundant proportional and integral control. Redundancy does not solve the problem of very different dynamic responses in different regions of space, with responses in some regions plagued by extreme sluggishness or extreme jitter. As the ultrasound rotor bumps into mechanical limits, in certain regions a bump trips the system into blocking oscillations. Recovery requires shutdown and re-initialization of the servo system, which can be problematic. If the rotor gets too far from its target position in highly nonlinear beacon coordinates, it can get "lost" and fail to find a path to the target coordinates. Even if local singularities in the beacon coordinate mapping are avoided entirely, this is no guarantee of convergence of the rotor from a distance away from a target set of coordinates. Where there is non-convergence, there is usually latchup. The complexity of software control compensations for a highly nonlinear and multidimensional electromagnetic sensing and drive system rapidly becomes unwieldy.
In the prior art, it was clearly believed that a relatively linear beacon coordinate mapping was not feasible in a practical winding topology for a system satisfying the constraints of transcranial Doppler ultrasound. To quote from U.S. Pat. No. 5,844,140, column 12, lines 48-53: "In a concrete example of a rotor for transcranial Doppler ultrasound, where clinical constraints call for windings confined to a small volume asymmetric to one side of the volume of rotor motion, the mapping from beacon coordinates to more familiar and convenient rotor coordinates is highly non-linear and non-orthogonal." The supposed necessity to work with such a mapping led to a system design that worked well only for small excursions from a central rotor position and angular orientation and that failed to function at and near singular points within its intended range. The option of adding redundant control coordinates, as was suggested in the prior art patent, has been shown to yield very limited performance improvements. A way out of the problems and limitations of the prior art system is to accomplish what was thought unfeasible: a mapping of beacon coordinates that are approximately linear and approximately orthogonal over the entire five-dimensional control volume required for applications like transcranial Doppler ultrasound. This is, of course, no merely mathematical mapping, but a description of the geometric electromagnetic performance of a collection of conductive windings. The following specification will show how to create such windings, interconnect them, drive them, and recover signals from them, to achieve such a beacon coordinate mapping. This will be achieved working within the geometric constraint that one side of the ultrasound cavity must be capable of placement on the skin with a side surface very close to the human ear--a constraint believed to necessitate an asymmetric winding configuration. Additional improvements in electronic topologies and methods for position detection and multidimensional servo control will be revealed.